Europe is fighting fires on all sides: Migrants pour in from north Africa. Ukraine teeters on the brink. And the scars of the global financial crisis are still healing.

The Greek people's resounding rejection of Europe's terms for a financial rescue demands a response.

An immediate one.

Greece will go bankrupt without money soon. That would almost certainly mean it has to abandon the euro -- the centerpiece of efforts by generations of European politicians to pull together a continent torn apart by war twice in the last century.

With so much at stake, why is it so hard to strike a deal?

Why doesn't Europe, whose leaders meet Tuesday in an emergency summit,just make it easier for Greece to cope with its enormous debt?

Unfortunately, it's not that simple. There are strong arguments pulling European leaders in both directions.

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It's about the euro

The euro was introduced in January 1999. Its architects believed it would boost Europe by making it easier to do business across borders, and help consumers get a better deal by allowing them to compare prices. It has become the most visible symbol of European integration.

But unlike other big currency unions, such as the U.S., the eurozone did not come with a pooling of political power or the creation of a big federal budget that could be used to help out poorer members.

Voters weren't ready for that. Instead, the 11 governments that launched the euro agreed to rules that, among other things, were supposed to keep each of them from borrowing too much. The aim was to make sure the currency was stable.

Since then, the rulebook has grown to cover how banks are regulated and how governments that get into trouble financially can be rescued. Countries such as Ireland, Portugal and Spain stuck to those rules in times of crisis -- and have seen their economies begin to grow again after painful bailout programs.

Much of that money has been put up by other governments in Europe, who are answerable to their voters for how it is spent. They don't understand why the rules should be bent, or even broken, for Greece. Nor why they should be writing off its debt, which would amount to one state subsidizing another.

Sigmar Gabriel, Germany's economy minister, said granting special treatment would be fatal for the currency. If Greece can get debt relief, why not others?

"That would be the end of the euro," he told reporters on Monday.

Some analysts say cutting Greece loose may even help the euro by allowing the remaining 18 countries to bind themselves even tighter together.

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High price to pay

But if Europe maintains a rigid stance in the long term interests of the euro, it risks watching an economic disaster unfold in Greece.

Cut off from all financial support, Greece would have to print its own currency, and inflation would likely soar -- making life even tougher for millions of Greeks who have already suffered years of hardship.

Indeed, European officials are already talking about how they might provide humanitarian aid, such as medicines and other essential goods, if Greece cannot afford the imports. Without it, social and political unrest could escalate.

The prospect of a failing state in southeastern Europe alarms policymakers from Brussels to Washington. Greece is a member of NATO, but has been flirting with Russia. And it is the gateway to Europe for many migrants fleeing war, terror and poverty in the Middle East and Africa.

The path to euro membership was supposed to be a one-way street. In fact, there's no rule book to manage a member country crashing out.

A domino effect is unlikely now. It's hard to imagine any other country choosing to follow Greece into the economic abyss, but a "Grexit" would take the eurozone into uncharted waters.

So the next time a heavily indebted country gets into trouble, it may find its membership of the euro called into question.

And finally, there's cold hard cash. Granting Greece debt relief may cost creditors 127 billion euros, most of that falling on Europe, according to RBS analysts. Letting the country go would cost at least 227 billion, they estimate.